I'd like to end the series by considering why this liberal concept of freedom also committed Shelley to such an emphasis on equality.
I think the answer goes something like this:
1. Shelley rejected the idea that human nature was tainted, i.e. that man was a fallen creature.
2. He believed instead that man had power over his own nature. It was human institutions that had corrupted this nature, and these could be reformed.
3. Once man was perfected he would return to his intended, natural condition of being good, free and equal.
4. In this condition, a utopia would emerge, a heaven on earth, in which human existence would be regenerated, with everything being made beautiful, in body and mind, and subject only to a pure universal love, unmotivated by any base concerns.
Man was corrupted, in Shelley's view, and denied this wonderful utopian existence, by acts of tyranny - the exercise of power over others. It was this that threw a "mask" over the world, hiding man's true nature from himself. In Shelley's own words:
Of virtuous soul commands not, nor obeys:
Power, like a desolating pestilence,
Pollutes whate'er it touches
And this is where freedom and equality become such great and noble (and inseparable) objectives for Shelley. The aim was to reach a condition in which there was no exercise of power over others. Shelley was so serious about this that he even portrayed God as a tyrant and a modified version of Satan as the hero who rebelled against the authority of God.
So try then to imagine how Shelley saw things. For him, what mattered was a fight for liberty against "tyranny" (defined as any exercise of power of one person over another) which therefore was also a fight for equality (for abolishing "distinctions" that gave one person some sort of standing vis-a-vis another person). Hence the twinning of freedom and equality.
Freedom and equality were the keys to establishing humanity's true condition of heaven on earth and so were supercharged in their significance.
It would be easy to criticise Shelley's world view as being unworkable or impractical. But more than this it deserves to be condemned for being, mostly, undesirable - a dystopia rather than a utopia.
If we return once more to Shelley's vision of what man would be like once the "mask" had been removed, and true freedom and equality revealed, we see the problem:
The loathsome mask has fallen, the man remains/ Sceptreless, free, uncircumscribed, but man/ Equal, unclassed, tribeless, and nationless,/ Exempt from awe, worship, degree, the king/ Over himself
What does it mean to be free in a Shelleyan sense? It means that nobody has power over me and that I am king over myself - an autonomous individual. My will is uncircumscribed. But to be free and equal in this sense also means that I am tribeless, nationless, Godless and churchless. Also abolished, as Shelley explains elsewhere, are biological sex and marriage.
Do I really want Shelleyan freedom? What about the meaning, identity and belonging that I derive from manhood, from membership of a communal tradition, and from stable family commitments?
Shelley wants us to move away from particular loves and loyalties, and the obligations and commitments that go with this, toward disinterested universal ones, which do not "encumber" us, but which also abstract, atomise and deracinate our own personhood, and which make human relationships shifting, uncertain and volatile.
The last point is evidenced in Shelley's own life. He wanted "pure" relationships, based not on exclusivity or jealousy, but this ended in the suicides of two women, including his first wife. Throughout his life, he "abandoned" quickly and frequently.
It is not that Shelley was wrong in just one respect, or that his system could be tweaked a little to make it viable and desirable. It is the larger approach that fails, the overall framework.